4 ON THE EFFECT OF THE INTEBNAL FRICTION OF FLUIDS
tion for buoyancy must be multiplied in order to give the whole effect of the air as deduced from observation. Four spheres, not quite 1J inch in diameter, gave as a mean ?i = 1*864, while three spheres, a little more than 2 inches in diameter, gave only 1'748. The latter were nearly of the same size as those with which Bessel, by a different method, had obtained &=0'946 or 0*956, which corresponds to ^ = 1'946 or T956. Among the " Additional Experiments " in the latter part of Baily's paper, is a set in which the pendulums consisted of plain cylindrical rods. With these pendulums it was found that n regularly increased, though according to an unknown law, as the diameter of the rod decreased. While a brass tube 1| inch in diameter gave n equal to about 2*3, a thin rod or thick wire only 0*072 inch in diameter gave for n a value as great as 7*530.
Mathematicians in the meanwhile were not idle, and several memoirs appeared about this time, of which the object was to determine from hydrodynamics the effect of a fluid on the motion of a pendulum. The first of these came from the pen of the celebrated Poisson. It was read before the French Academy on the 22nd of August 1831, and is printed in the llth Volume of the Memoirs. In this paper, Poisson considers the case of a sphere suspended by a fine wire, and oscillating in the air, or in any gas. He employs the ordinary equations of motion of an elastic fluid, simplified by neglecting the terms which involve the square of the velocity; but in the end, in adapting his solution to practice, he neglects, as insensible, the terms by which alone the action of an elastic differs from that of an incompressible fluid, so that the result thus simplified is equally applicable to fluids of both classes. He finds that when insensible quantities are neglected n = l'5, so that the mass which we must suppose added to that of the pendulum is equal to half the mass of the fluid displaced. This result does not greatly differ from the results obtained experimentally by Bessel in the case of spheres oscillating in water, but differs materially from the result he had obtained for air. It agrees pretty closely with some experiments which had been performed about fifty years before by Dubuat, who had in fact anticipated Bessel in shewing that the time of vibration of a pendulum vibrating in a fluid would be affected by the inertia of the fluid as well as by its density. Dubuat's labours on this subject had been altogether overlooked by those who were engaged in pendulum experiments ;